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m x n grid in a rectangle, no of rectangles wanted

Source: Flanders Math Olympiad 1987 p1

December 24, 2022
combinatorial geometrycombinatorics

Problem Statement

A rectangle ABCDABCD is given. On the side ABAB, nn different points are chosen strictly between AA and BB. Similarly, mm different points are chosen on the side ADAD. Lines are drawn from the points parallel to the sides. How many rectangles are formed in this way? (One possibility is shown in the figure.) https://cdn.artofproblemsolving.com/attachments/0/1/dcf48e4ce318fdcb8c7088a34fac226e26e246.png